THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 49

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X₁,X₂,X₃,and X₄ be a random sample of observations from a population with mean μ and variance σ².Consider the following two point estimators of μ:
₁ = 0.10 X₁ + 0.20 X₂ + 0.40 X₃ + 0.30 X₄,and
₂ = 0.25 X₁ + 0.25 X₂ + 0.30 X₃ + 0.20 X₄
-Raising in-state and out-of-state tuition is supposed to reduce the number of students in state supported universities.The registrar of a university wants to estimate the proportion P of students who are paying for out-of-state tuition on the installment plan (to later be compared with in-state installment plan payers).A random sample of 80 students who live out-of-state is taken and 50 of them pay tuition on the installment plan.Find a 99-percent confidence interval for P,based on these data.

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Definitions:

Payment Installments

Regular, partial payments made over a period of time to settle a debt or purchase price, often involving interest charges.

Practitioner

An individual involved professionally in the practice of a particular occupation, often in the healthcare and medicinal fields.

Initial Letter

The first letter of a word, sentence, or paragraph, which can sometimes be capitalized or stylized for emphasis or decorative purposes.

Days Past Due

The number of days that have elapsed since a payment was due, often used in financial contexts to indicate overdue payments.